Toronto M5S 3G4 Canada mcosmin,gpenn @cs.toronto.edu Abstract This paper introduces an indexing method based on static analysis of grammar rules and type signatures for typed feature str
Trang 1Optimizing Typed Feature Structure Grammar Parsing through
Non-Statistical Indexing Cosmin Munteanu and Gerald Penn
University of Toronto
10 King’s College Rd
Toronto M5S 3G4 Canada mcosmin,gpenn @cs.toronto.edu
Abstract
This paper introduces an indexing method based on
static analysis of grammar rules and type signatures
for typed feature structure grammars (TFSGs) The
static analysis tries to predict at compile-time which
feature paths will cause unification failure during
parsing at run-time To support the static analysis,
we introduce a new classification of the instances
of variables used in TFSGs, based on what type of
structure sharing they create The indexing actions
that can be performed during parsing are also
enu-merated Non-statistical indexing has the
advan-tage of not requiring training, and, as the
evalua-tion using large-scale HPSGs demonstrates, the
im-provements are comparable with those of statistical
optimizations Such statistical optimizations rely
on data collected during training, and their
perfor-mance does not always compensate for the training
costs
1 Introduction
Developing efficient all-paths parsers has been a
long-standing goal of research in computational
lin-guistics One particular class still in need of
pars-ing time improvements is that of TFSGs While
simpler formalisms such as context-free grammars
(CFGs) also face slow all-paths parsing times when
the size of the grammar increases significantly,
TF-SGs (which generally have fewer rules than
large-scale CFGs) become slow as a result of the
com-plex structures used to describe the grammatical
egories In HPSGs (Pollard and Sag, 1994), one
cat-egory description could contain hundreds of feature
values This has been a barrier in transferring
CFG-successful techniques to TFSG parsing
For TFSG chart parsers, one of the most
time-consuming operations is the retrieval of categories
from the chart during rule completion (closing of
constituents in the chart under a grammar rule)
Looking in the chart for a matching edge for a
daughter is accomplished by attempting unifications
with edges stored in the chart, resulting in many
failed unifications The large and complex structure
of TFS descriptions (Carpenter, 1992) leads to slow unification times, affecting the parsing times Thus, failing unifications must be avoided during retrieval from the chart
To our knowledge, there have been only four methods proposed for improving the retrieval com-ponent of TFSG parsing One (Penn and Munteanu, 2003) addresses only the cost of copying large cate-gories, and was found to reduce parsing times by an average of 25% on a large-scale TFSG (MERGE) The second, a statistical method known as quick-check (Malouf et al., 2000), determines the paths that are likely to cause unification failure by pro-filing a large sequence of parses over representa-tive input, and then filters unifications at run-time
by first testing these paths for type consistency This was measured as providing up to a 50% im-provement in parse times on the English Resource Grammar (Flickinger, 1999, ERG) The third (Penn, 1999b) is a similar but more conservative approach that uses the profile to re-order sister feature values
in the internal data structure This was found to im-prove parse times on the ALE HPSG by up to 33% The problem with these statistical methods is that the improvements in parsing times may not jus-tify the time spent on profiling, particularly during grammar development The static analysis method introduced here does not use profiling, although it does not preclude it either Indeed, an evaluation of statistical methods would be more relevant if mea-sured on top of an adequate extent of non-statistical optimizations Although quick-check is thought to produce parsing time improvements, its evaluation used a parser with only a superficial static analysis
of chart indexing
That analysis, rule filtering (Kiefer et al., 1999), reduces parse times by filtering out mother-daughter unifications that can be determined to fail at compile-time True indexing organizes the data (in this case, chart edges) to avoid unnecessary re-trievals altogether, does not require the operations that it performs to be repeated once full unification
Trang 2is deemed necessary, and offers the support for
eas-ily adding information extracted from further static
analysis of the grammar rules, while maintaining
the same indexing strategy Flexibility is one of the
reasons for the successful employment of indexing
in databases (Elmasri and Navathe, 2000) and
auto-mated reasoning (Ramakrishnan et al., 2001)
In this paper, we present a general scheme for
in-dexing TFS categories during parsing (Section 3)
We then present a specific method for statically
an-alyzing TFSGs based on the type signature and the
structure of category descriptions in the grammar
rules, and prove its soundness and completeness
(Section 4.2.1) We describe a specific indexing
strategy based on this analysis (Section 4), and
eval-uate it on two large-scale TFSGs (Section 5) The
result is a purely non-statistical method that is
com-petitive with the improvements gained by statistical
optimizations, and is still compatible with further
statistical improvements
2 TFSG Terminology
TFSs are used as formal representatives of rich
grammatical categories In this paper, the
formal-ism from (Carpenter, 1992) will be used A TFSG
is defined relative to a fixed set of types and set of
features, along with constraints, called
appropriate-ness conditions These are collectively known as
the type signature (Figure 3) For each type,
ap-propriateness specifies all and only the features that
must have values defined in TFSs of that type It
also specifies the types of the values that those
fea-tures can take The set of types is partially ordered,
and has a unique most general type ( – “bottom”)
This order is called subsumption ( ): more specific
(higher) types inherit appropriate features from their
more general (lower) supertypes Two types t1 and
t2 unify (t1 t2
) iff they have a least upper bound
in the hierarchy Besides a type signature, TFSGs
contain a set of grammar (phrase) rules and lexical
descriptions A simple example of a lexical
descrip-tion is: john SYNSEM: SYN: np SEM: j , while
an example of a phrase rule is given in Figure 1
SYN: s SEM:V PSem AGENT: NPSem
SYN: np AGR: Agr SEM: NPSem ,
SYN: vp AGR: Agr SEM: V PSem
Figure 1: A phrase rule stating that the syntactic category
s can be combined from np and vp if their values for
agr are the same The semantics of s is that of the verb
phrase, while the semantics of the noun phrase serves as
agent.
2.1 Typed Feature Structures
A TFS (Figure 2) is like a recursively defined record
in a programming language: it has a type and fea-tures with values that can be TFSs, all obeying the appropriateness conditions of the type signature TFSs can also be seen as rooted graphs, where arcs correspond to features and nodes to substructures A node typing functionθq associates a type to every
node q in a TFS Every TFS F has a unique starting
or root node, q F For a given TFS, the feature value partial functionδ f q specifies the node reachable
from q by feature f when one exists The path value
partial functionδπ q specifies the node reachable
from q by following a path of features πwhen one exists TFSs can be unified as well The result repre-sents the most general consistent combination of the information from two TFSs That information in-cludes typing (by unifying the types), feature values (by recursive unification), and structure sharing (by
an equivalence closure taken over the nodes of the arguments) For large TFSs, unification is compu-tationally expensive, since all the nodes of the two TFSs are visited In this process, many nodes are collapsed into equivalence classes because of
struc-ture sharing A node x in a TFS F with root q F and
a node x in a TFS F with root q F are equivalent ( ) with respect to F F iff x q F and x q F,
or if there is a pathπsuch thatδF F π q F x and
δF F π q F
NUMBER:
PERSON:
GENDER: masculine
third [1]singular
NUMBER:
PERSON:
GENDER:
third neuter [1]
throwing
THROWER: index
THROWN: index
Figure 2: A TFS Features are written in uppercase, while types are written with bold-face lowercase
Struc-ture sharing is indicated by numerical tags, such as [1].
THROWER:
THROWN:
index index
masculine feminine neuter singular plural first second third
num
PERSON: GENDER: NUMBER:
pers num gend
Figure 3: A type signature For each type, appropriate-ness declares the features that must be defined on TFSs
of that type, along with the type restrictions applying to their values.
Trang 32.2 Structure Sharing in Descriptions
TFSGs are typically specified using descriptions,
which logically denote sets of TFSs Descriptions
can be more terse because they can assume all of
the information about their TFSs that can be
in-ferred from appropriateness Each non-disjunctive
description can be associated with a unique most
general feature structure in its denotation called a
most general satisfier (MGSat). While a formal
presentation can be found in (Carpenter, 1992), we
limit ourselves to an intuitive example: the TFS
from Figure 2 is the MGSat of the description:
throwing THROWER: PERSON: third NUMBER:
singular Nr GENDER: masculine THROWN:
PERSON: third NUMBER: NrGENDER: neuter
Descriptions can also contain variables, such as Nr.
Structure sharing is enforced in descriptions
through the use of variables In TFSGs, the scope
of a variable extends beyond a single description,
re-sulting in structure sharing between different TFSs
In phrase structure rules (Figure 1), this sharing
can occur between different daughter categories in
a rule, or between a mother and a daughter Unless
the term description is explicitly used, we will use
“mother” and “daughter” to refer to the MGSat of a
mother or daughter description
We can classify instances of variables based on
what type of structure sharing they create
Inter-nal variables are the variables that represent
inter-nal structure sharing (such as in Figure 2) The
oc-currences of such variables are limited to a single
category in a phrase structure rule External
vari-ables are the varivari-ables used to share structure
be-tween categories If a variable is used for
struc-ture sharing both inside a category and across
cat-egories, then it is also considered an external
vari-able For a specific category, two kinds of external
variable instances can be distinguished, depending
on their occurrence relative to the parsing control
strategy: active external variables and inactive
ex-ternal variables Active exex-ternal variables are
in-stances of external variables that are shared between
the description of a category D and one or more
de-scriptions of categories in the same rule as D
vis-ited by the parser before D as the rule is extended
(completed) Inactive external variables are the
ternal variable instances that are not active For
ex-ample, in bottom-up left-to-right parsing, all of a
mother’s external variable instances would be active
because, being external, they also occur in one of
the daughter descriptions Similarly, all of the
left-most daughter’s external variable instances would
be inactive because this is the first description used
by the parser In Figure 1, Agr is an active external
variable in the second daughter, but it is inactive in the first daughter
The active external variable instances are im-portant for path indexing (Section 4.2), because they represent the points at which the parser must copy structure between TFSs They are therefore substructures that must be provided to a rule by the parsing chart if these unifications could poten-tially fail They also represent shared nodes in the
MGSats of a rule’s category descriptions In our
definitions, we assume without loss of generality that parsing proceeds bottom-up, with left-to-right
of rule daughters This is the ALE system’s (Car-penter and Penn, 1996) parsing strategy
Definition 1 If D1 D n are daughter de-scriptions in a rule and the rules are extended from left to right, then ExtMGSatD i is the set of nodes shared between MGSatD i and MGSatD1
de-scription M, ExtMGSatM is the set of nodes shared with any daughter in the same rule.
Because the completion of TFSG rules can cause the categories to change in structure (due to exter-nal variable sharing), we need some extra notation
to refer to a phrase structure rule’s categories at dif-ferent times during a single application of that rule By
M we symbolize the mother M after M’s rule is
completed (all of the rule’s daughters are matched with edges in the chart)
D symbolizes the
daugh-ter D afdaugh-ter all daughdaugh-ters to D’s left in D’s rule were
unified with edges from the chart An important
re-lation exists between M and
M: if q M is M’s root and
q Mis
M’s root, then
x M
x
M such that πfor whichδπ q M x andδπ
q M
x, θx θ
x
In other words, extending the rule extends the in-formation states of its categories monotonically A
similar relation exists between D and
D The set of
all nodes x in M such that πfor whichδπ q M x
andδπ
q M
x will be denoted by
x
1(and
like-wise for nodes in D) There may be more than one
node in
x
1because of unifications that occur
dur-ing the extension of M to
M.
3 The Indexing Timeline
Indexing can be applied at several moments dur-ing parsdur-ing We introduce a general strategy for in-dexed parsing, with respect to what actions should
be taken at each stage
Three main stages can be identified The first one consists of indexing actions that can be taken off-line (along with other optimizations that can be performed at compile-time) The second and third stages refer to actions performed at run time
Trang 4Stage 1 In the off-line phase, a static analysis
of grammar rules can be performed The complete
content of mothers and daughters may not be
ac-cessible, due to variables that will be instantiated
during parsing, but various sources of information,
such as the type signature, appropriateness
specifi-cations, and the types and features of mother and
daughter descriptions, can be analyzed and an
ap-propriate indexing scheme can be specified This
phase of indexing may include determining: (1a)
which daughters in which rules will certainly not
unify with a specific mother, and (1b) what
informa-tion can be extracted from categories during parsing
that can constitute indexing keys It is desirable to
perform as much analysis as possible off-line, since
the cost of any action taken during run time
pro-longs the parsing time
Stage 2 During parsing, after a rule has been
completed, all variables in the mother have been
ex-tended as far as they can be before insertion into
the chart This offers the possibility of further
in-vestigating the mother’s content and extracting
sup-plemental information from the mother that
con-tributes to the indexing keys However, the choice
of such investigative actions must be carefully
stud-ied, since it might burden the parsing process
Stage 3. While completing a rule, for each
daughter a matching edge is searched in the chart
At this moment, the daughter’s active external
vari-ables have been extended as far as they can be
be-fore unification with a chart edge The information
identified in stage (1b) can be extracted and unified
as a precursor to the remaining steps involved in
cat-egory unification These steps also take place at this
stage
4 TFSG Indexing
To reduce the time spent on failures when
search-ing for an edge in the chart, each edge (edge’s
cat-egory) has an associated index key which uniquely
identifies the set of daughter categories that can
po-tentially match it When completing a rule, edges
unifying with a specific daughter are searched for in
the chart Instead of visiting all edges in the chart,
the daughter’s index key selects a restricted number
of edges for traversal, thus reducing the number of
unification attempts
The passive edges added to the chart represent
specializations of rules’ mothers When a rule is
completed, its mother M is added to the chart
ac-cording to M’s indexing scheme, which is the set of
index keys of daughters that might possibly unify
with M The index is implemented as a hash, where
the hash function applied to a daughter yields the
daughter’s index key (a selection of chart edges)
For a passive edge representing M, M’s
index-ing scheme provides the collection of hash entries where it will be added
Each daughter is associated with a unique index key During parsing, a specific daughter is searched for in the chart by visiting only those edges that have
a matching key, thus reducing the time needed for traversing the chart The index keys can be com-puted off-line (when daughters are indexed by posi-tion), or during parsing
4.1 Positional Indexing
In positional indexing, the index key for each daughter is represented by its position (rule number and daughter position in the rule) The structure of the index can be de-termined at compile-time (first stage) For
each mother M in the grammar, a collection
LM R i D j daughters that can match M is
created (M’s indexing scheme), where each element
ofLM represents the rule number R iand daughter
position D j inside rule R i (1 j arityR i ) of a
category that can match with M.
For TFSGs it is not possible to compute off-line the exact list of mother-daughter matching pairs, but
it is possible to rule out certain non-unifiable pairs before parsing — a compromise that pays off with a very low index management time
During parsing, each time an edge (representing
a rule’s mother M) is added to the chart, it is
in-serted into the hash entries associated with the po-sitions R i D j from the list LM (the number of
entries where M is inserted is LM ) The entry associated with the key R i D j will contain only categories that can possibly unify with the daughter
at position R i D j in the grammar
Because our parsing algorithm closes categories depth-first under leftmost daughter matching, only
daughters D i with i 2 are searched for in the chart (and consequently, indexed) We used the EFD-based modification of this algorithm (Penn and Munteanu, 2003), which needs no active edges, and requires a constant two copies per edges, rather than the standard one copy per retrieval found in Prolog parsers Without this, the cost of copying TFS categories would have overwhelmed the bene-fit of the index
4.2 Path Indexing
Path indexing is an extension of positional index-ing Although it shares the same underlying prin-ciple as the path indexing used in automated rea-soning (Ramakrishnan et al., 2001), its functionality
is related to quick check: extract a vector of types
Trang 5from a mother (which will become an edge) and a
daughter, and test the unification of the two vectors
before attempting to unify the edge and the
daugh-ter Path indexing differs from quick-check in that
it identifies these paths by a static analysis of
gram-mar rules, performed off-line and with no training
required Path indexing is also built on top of
po-sitional indexing, therefore the vector of types can
be different for each potentially unifiable
mother-daughter pair
4.2.1 Static Analysis of Grammar Rules
Similar to the abstract interpretation used in
pro-gram verification (Cousot and Cousot, 1992),
the static analysis tries to predict a run-time
phenomenon (specifically, unification failures) at
compile-time It tries to identify nodes in a mother
that carry no relevant information with respect to
unification with a particular daughter For a mother
M unifiable with a daughter D, these nodes will
be grouped in a set StaticCutM D Intuitively,
these nodes can be left out or ignored while
com-puting the unification of
M and
D The StaticCut
can be divided into two subsets: StaticCutM D
RigidCutM D VariableCutM D
The RigidCut represents nodes that can be left out
because neither they, nor one of theirδπ-ancestors,
can have their type values changed by means of
ex-ternal variable sharing The VariableCut represents
nodes that are either externally shared, or have an
externally shared ancestor, but still can be left out
Definition 2 RigidCutM D is the largest subset
of nodes x M such that,
y D for which x y:
1 x ExtM , y ExtD ,
2.
x M s.t. πs.t.δπ x x, x ExtM , and
3.
y D s.t. πs.t.δπ y y, y ExtD .
Definition 3 VariableCut is the largest subset of
nodes x M such that:
1 x RigidCutM D , and
2.
y D for which x y,
s θx
t θy ,
s t exists.
In words, a node can be left out even if it is
ex-ternally shared (or has an exex-ternally shared
ances-tor) if all possible types this node can have unify
with all possible types its corresponding nodes in
D can have Due to structure sharing, the types of
nodes in M and D can change during parsing, by
being specialized to one of their subtypes
Condi-tion 2 ensures that the types of these nodes will
re-main compatible (have a least upper bound), even if
they specialize during rule completion An intuitive
example (real-life examples cannot be reproduced
here — a category in a typical TFSG can have
hun-dreds of nodes) is presented in Figure 4
y2
y1
y3 y5 t1
y4 t1
t5 F:
G:
H:
G: K:
D
x1
x4
F: H:
G:
I:
t3 t1
G:t1 H:t6 F:t6
K:t1 I:t3
t1
t2
J:t5
t6
t0
T
t8
M
Figure 4: Given the above type signature, mother M and daughter D (externally shared nodes are pointed to by dashed arrows), nodes x1x2 and x3from M can be left out when unifying M with D during parsing x1and x3
RigidCutMD , while x2
VariableCutMD ( θ y2
can promote only to t7, thus x2 and y2 will always be
compatible) x4is not included in the StaticCut, because
if θ y5 promotes to t5, then θ y4 will promote to t5(not
unifiable with t3).
When computing the unification between a mother and a daughter during parsing, the same out-come (success or failure) will be reached by using
a reduced representation of the mother (
MsD), with
nodes in StaticCutM D removed from
M.
Proposition 1 For a mother M and a daughter D,
if M D
before parsing, and
M (as an edge in the chart) and
D exist, then during parsing: (1)
MsD
D
M
D
, (2)
MsD
D
M
D Proof The second part (
MsD
D
M
D )
of Proposition 1 has a straightforward proof: if
MsD
D , then
z
MsD
D such that t for
which
x
z t θ
x Since
MsD
M,
z
M
D such that t for which
x
z t θ
x , and therefore,
M
D The first part of the proposition will be proven by showing that
z
M
D, a consistent type can be
assigned to
z , where
z is the set of nodes in
M
and
D equivalent to
z with respect to the unification
of
M and
D.1
Three lemmata need to be formulated:
Lemma 1 If
x
M and x
x
1, thenθ
x θx Similarly, for
y
D, y
y
1,θ
y θy .
Lemma 2 If types t0 t1 t n are such that
t0
t0
, then t t0such that
i
1 Because we do not assume inequated TFSs (Carpenter, 1992) here, unification failure must result from type inconsis-tency.
Trang 6Lemma 3 If
x
M and
y
D for which
x
y, then
x
1
y
1such that x y.
In proving the first part of Proposition 1, four
cases are identified: Case A:
z
M 1 and
z
D 1, Case B:
z
M 1 and
z
D 1, Case C:
z
M 1 and
z
D 1,
Case D:
z
M 1 and
z
D 1 Case A
is trivial, and D is a generalization of B and C
Case B It will be shown that t Type such that
y
z
D and for
x
z
M, t θ
y and
t θ
x
Subcase B.i:
x
M
x
MsD
y
z
D,
y
x. Therefore, according to Lemma 3, x
x
1
y
1 such that x y Thus, according
to Condition 2 of Definition 3,
s θy
t θx ,
s t
But according to Lemma 1,θ
y θy and
θ
x θx Therefore,
y
z
D,
s θ
y ,
t θ
x , s t
, and hence,
y
z
D
t
θ
x t θ
y
Thus, according to Lemma 2, t
θ
x
y
z
D, t θ
y
Subcase B.ii:
x
M
x
MsD Since
MsD
D
,
x such that
y
z
D, t θ
y
Case C It will be shown that t θ
y such that
x
z , t θ
x Let
y
z
D The
set
z
M can be divided into two subsets: S ii
x
z
M
x
MsD
, and S i
x
z
M
x
M
x
MsD , and x VariableCutM D If x
were in RigidCutM D , then necessarily
z
M
would be 1 Since S ii
MsD and
MsD
D
, then
y such that
x S ii t θ
x (*) How-ever,
x S ii,
x
y. Therefore, according to Lemma 3,
x S ii x
x
1
y
1 such that
x y Thus, since x VariableCutM D ,
Condi-tion 2 of DefiniCondi-tion 3 holds, and therefore,
accord-ing to Lemma 1,
s1 θ
x
s2 θ
y s1 s2
More than this, since t θ
y (for the type t from (*)),
s1 θ
x
s2 t s1 s2
, and hence,
s2
t s2 θ
x
Thus, according to Lemma 2 and to
(*), t t θ
y such that
x S ii t θ
x Thus,
t such that
x
z , t θ
x While Proposition 1 could possibly be used by
grammar developers to simplify TFSGs themselves
at the source-code level, here we only exploit it for
internally identifying index keys for more efficient
chart parsing with the existing grammar There may
be better static analyses, and better uses of this static
analysis In particular, future work will focus on
us-ing static analysis to determine smaller
representa-tions (by cutting nodes in Static Cuts) of the chart
edges themselves
4.2.2 Building the Path Index
The indexing schemes used in path indexing are built on the same principles as those in positional indexing The main difference is the content of the indexing keys, which now includes a third element
Each mother M has its indexing scheme defined as:
LM R i D j V ij The pair R i D j is the
po-sitional index key (as in popo-sitional indexing), while
V ij is the path index vector containing type values extracted from M A different set of types is
ex-tracted for each mother-daughter pair So, path in-dexing uses a two-layer inin-dexing method: the po-sitional key for daughters, and types extracted from the typed feature structure Each daughter’s index key is now given byLD j R i V ij , where R i
is the rule number of a potentially matching mother,
and V ij is the path index vector containing types
ex-tracted from D j The types extracted for the indexing vectors
are those of nodes found at the end of indexing
paths A path π is an indexing path for a mother-daughter pair M D iff: (1)πis defined for both M and D, (2) x StaticCutM D f s.t.δ f x
δπ q M (q M is M’s root), and (3) δπ q M
StaticCutM D Indexing paths are the “frontiers”
of the non-statically-cut nodes of M.
A similar key extraction could be performed dur-ing Stage 2 of indexdur-ing (as outlined in Section 3), using
M rather than M We have found that this
on-line path discovery is generally too expensive to be performed during parsing, however
As stated in Proposition 1, the nodes in
StaticCutM D do not affect the success/failure of
M
D. Therefore, the types of first nodes
not included in StaticCutM D along each path
π that stems from the root of M and D are
in-cluded in the indexing key, since these nodes might contribute to the success/failure of the
unifica-tion It should be mentioned that the vectors V ij
are filled with values extracted from
M after M’s
rule is completed, and from
D after all
daugh-ters to the left of D are unified with edges in the
chart As an example, assuming that the index-ing paths are THROWER:PERSON, THROWN, and
TFS shown in Figure 2 isthird index neuter
4.2.3 Using the Path Index
Inserting and retrieving edges from the chart using path indexing is similar to the general method pre-sented at the beginning of this section The first layer of the index is used to insert a mother as
an edge into appropriate chart entries, according to the positional keys for the daughters it can match
Trang 7Along with the mother, its path index vector is
in-serted into the chart
When searching for a matching edge for a
daugh-ter, the search is restricted by the first indexing layer
to a single entry in the chart (labeled with the
posi-tional index key for the daughter) The second layer
restricts searches to the edges that have a
compati-ble path index vector The compatibility is defined
as type unification: the type pointed to by the
el-ement V ijn of an edge’s vector V ij should unify
with the type pointed to by the element V ijn of the
path index vector V ij of the daughter on position D j
in a rule R i
5 Experimental Evaluation
Two TFSGs were used to evaluate the performance
of indexing: a pre-release version of the MERGE
grammar, and the ALE port of the ERG (in its final
form) MERGE is an adaptation of the ERG which
uses types more conservatively in favour of
rela-tions, macros and complex-antecedent constraints
This pre-release version has 17 rules, 136 lexical
items, 1157 types, and 144 introduced features The
ERG port has 45 rules, 1314 lexical entries, 4305
types and 155 features MERGE was tested on 550
sentences of lengths between 6 and 16 words,
ex-tracted from the Wall Street Journal annotated parse
trees (where phrases not covered by MERGE’s
vo-cabulary were replaced by lexical entries having the
same parts of speech), and from MERGE’s own
test corpus ERG was tested on 1030 sentences of
lengths between 6 and 22 words, extracted from the
Brown Corpus and from the Wall Street Journal
an-notated parse trees
Rather than use the current version of ALE, TFSs
were encoded as Prolog terms as prescribed in
(Penn, 1999a), where the number of argument
po-sitions is the number of colours needed to colour
the feature graph This was extended to allow for
the enforcement of type constraints during TFS
uni-fication Types were encoded as attributed variables
in SICStus Prolog (Swedish Institute of Computer
Science, 2004)
5.1 Positional and path indexing evaluation
The average and best improvements in parsing times
of positional and path indexing over the same
EFD-based parser without indexing are presented in
Ta-ble 1 The parsers were implemented in SICStus
3.10.1 for Solaris 8, running on a Sun Server with 16
GB of memory and 4 UltraSparc v.9 processors at
1281 MHz For MERGE, parsing times range from
10 milliseconds to 1.3 seconds For ERG, parsing
times vary between 60 milliseconds and 29.2
sec-onds
Positional Index Path Index
Table 1: Parsing time improvements of positional and path indexing over the non-indexed EFD parser.
5.2 Comparison with statistical optimizations
Non-statistical optimizations can be seen as a first step toward a highly efficient parser, while statistical optimization can be applied as a second step How-ever, one of the purposes of non-statistical index-ing is to eliminate the burden of trainindex-ing while of-fering comparable improvements in parsing times
A quick-check parser was also built and evaluated and the set-up times for the indexed parsers and the quick-check parser were compared (Table 2) Quick-check was trained on a 300-sentence training corpus, as prescribed in (Malouf et al., 2000) The training corpus included 150 sentences also used in testing The number of paths in path indexing is dif-ferent for each mother-daughter pair, ranging from
1 to 43 over the two grammars
Table 2: The set-up times for non-statistically indexed parsers and statistically optimized parsers for MERGE.
As seen in Table 3, quick-check alone surpasses positional and path indexing for the ERG How-ever, it is outperformed by them on the MERGE, recording slower times than even the baseline But the combination of quick-check and path indexing
is faster than quick-check alone on both grammars Path indexing at best provided no decrease in per-formance over positional indexing alone in these ex-periments, attesting to the difficulty of maintaining efficient index keys in an implementation
Table 3: Comparison of average improvements over non-indexed parsing among all parsers.
The quick-check evaluation presented in (Malouf
et al., 2000) uses only sentences with a length of
at most 10 words, and the authors do not report the set-up times Quick-check has an additional advan-tage in the present comparison, because half of the training sentences were included in the test corpus While quick-check improvements on the ERG confirm other reports on this method, it must be
Trang 8Grammar Successful Failed unifications Failure rate reduction (vs no index)
Table 4: The number of successful and failed unifications for the non-indexed, positional indexing, path indexing, and quick-check parsers, over MERGE and ERG (collected on the slowest sentence in the corresponding test sets.)
noted that quick-check appears to be parochially
very well-suited to the ERG (indeed quick-check
was developed alongside testing on the ERG)
Al-though the recommended first 30 most probable
failure-causing paths account for a large part of
the failures recorded in training on both grammars
(94% for ERG and 97% for MERGE), only 51 paths
caused failures at all for MERGE during training,
compared to 216 for the ERG Further training with
quick-check for determining a better vector length
for MERGE did not improve its performance
This discrepancy in the number of failure-causing
paths could be resulting in an overfitted quick-check
vector, or, perhaps the 30 paths chosen for MERGE
really are not the best 30 (quick-check uses a greedy
approximation) In addition, as shown in Table 4,
the improvements made by quick-check on the ERG
are explained by the drastic reduction of (chart
look-up) unification failures during parsing relative to the
other methods It appears that nothing short of a
drastic reduction is necessary to justify the overhead
of maintaining the index, which is the largest for
quick-check because some of its paths must be
tra-versed at run-time — path indexing only uses paths
available at compile-time in the grammar source
Note that path indexing outperforms quick-check on
MERGE in spite of its lower failure reduction rate,
because of its smaller overhead
6 Conclusions and Future Work
The indexing method proposed here is suitable for
several classes of unification-based grammars The
index keys are determined statically and are based
on an a priori analysis of grammar rules A
ma-jor advantage of such indexing methods is the
elim-ination of the lengthy training processes needed
by statistical methods Our experimental
evalu-ation demonstrates that indexing by static
analy-sis is a promising alternative to optimizing parsing
with TFSGs, although the time consumed by on-line
maintenance of the index is a significant concern —
echoes of an observation that has been made in
ap-plications of term indexing to databases and
pro-gramming languages (Graf, 1996) Further work
on efficient implementations and data structures is
therefore required Indexing by static analysis of
grammar rules combined with statistical methods
also can provide a higher aggregate benefit
The current static analysis of grammar rules used
as a basis for indexing does not consider the effect
of the universally quantified constraints that typi-cally augment the signature and grammar rules Fu-ture work will investigate this extension as well
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Structure sharing is enforced in descriptions
through the use of variables In TFSGs, the scope
of a variable extends beyond a single description,
re-sulting in structure. .. represent the points at which the parser must copy structure between TFSs They are therefore substructures that must be provided to a rule by the parsing chart if these unifications could poten-tially